Optimal pricing strategy:How to sell to strategic consumers?

Technological advances are preparing consumers to plan their purchases strategically. Selling to strategic consumers at a fixed price forgoes the profit from salvaging inventory, whereas high-low pricing, as a ubiquitous pricing strategy, is costly due to the offered markdown discount. This research explores the overall impact of consumer's strategic buying behaviour on a pricing strategy, and identifies conditions where fixed pricing, strategic high pricing, or high-low pricing is the best approach by analytically comparing the profits of the three pricing strategies. Our results show that high-low pricing is appropriate only if the offered markdown discount is relatively small. If strategic consumers have a small population and the needed markdown discount is relatively large, retailers can ignore strategic buying behaviour and sell products at a fixed price. Our results emphasize that the markdown discount for clearance sales and the market structure of heterogeneous consumers play vital roles in determining the optimal pricing strategy

From Stream to Pool: Dynamic Pricing Beyond i.i.d. Arrivals

The dynamic pricing problem has been extensively studied under the \textbf{stream} model: A stream of customers arrives sequentially, each with an independently and identically distributed valuation. However, this formulation is not entirely reflective of the real world. In many scenarios, high-valuation customers tend to make purchases earlier and leave the market, leading to a \emph{shift} in the valuation distribution. Thus motivated, we consider a model where a \textbf{pool} of $n$ non-strategic unit-demand customers interact repeatedly with the seller. Each customer monitors the price intermittently according to an independent Poisson process and makes a purchase if the observed price is lower than her \emph{private} valuation, whereupon she leaves the market permanently. We present a minimax \emph{optimal} algorithm that efficiently computes a non-adaptive policy which guarantees a $1/k$ fraction of the optimal revenue, given any set of $k$ prices. Moreover, we present an adaptive \emph{learn-then-earn} policy based on a novel \emph{debiasing} approach, and prove an $\tilde O(kn^{3/4})$ regret bound. We further improve the bound to $\tilde O(k^{3/4} n^{3/4})$ using martingale concentration inequalities

Solving Practical Dynamic Pricing Problems with Limited Demand Information

Dynamic pricing problems have received considerable attention in the operations management literature in the last two decades. Most of the work has focused on structural results and managerial insights using stylized models without considering business rules and issues commonly encountered in practice. While these models do provide general, high-level guidelines for managers in practice, they may not be able to generate satisfactory solutions to practical problems in which business norms and constraints have to be incorporated. In addition, most of the existing models assume full knowledge about the underlying demand distribution. However, demand information can be very limited for many products in practice, particularly, for products with short life-cycles (e.g., fashion products). In this dissertation, we focus on dynamic pricing models that involve selling a fixed amount of initial inventory over a fixed time horizon without inventory replenishment. This class of dynamic pricing models have a wide application in a variety of industries. Within this class, we study two specific dynamic pricing problems with commonly-encountered business rules and issues where there is limited demand information. Our objective is to develop satisfactory solution approaches for solving practically sized problems and derive managerial insights. This dissertation consists of three parts. We first present a survey of existing pricing models that involve one or multiple sellers selling one or multiple products, each with a given initial inventory, over a fixed time horizon without inventory replenishment. This particular class of dynamic pricing problems have received substantial attention in the operations management literature in recent years. We classify existing models into several different classes, present a detailed review on the problems in each class, and identify possible directions for future research. We then study a markdown pricing problem that involves a single product and multiple stores. Joint inventory allocation and pricing decisions have to be made over time subject to a set of business rules. We discretize the demand distribution and employ a scenario tree to model demand correlation across time periods and among the stores. The problem is formulated as a MIP and a Lagrangian relaxation approach is proposed to solve it. Extensive numerical experiments demonstrate that the solution approach is capable of generating close-to-optimal solutions in a short computational time. Finally, we study a general dynamic pricing problem for a single store that involves two substitutable products. We consider both the price-driven substitution and inventory-driven substitution of the two products, and investigate their impacts on the optimal pricing decisions. We assume that little demand information is known and propose a robust optimization model to formulate the problem. We develop a dynamic programming solution approach. Due to the complexity of the DP formulation, a fully polynomial time approximation scheme is developed that guarantees a proven near optimal solution in a manageable computational time for practically sized problems. A variety of managerial insights are discussed

Dynamic Pricing in the Presence of Social Learning and Strategic Consumers

When a product of uncertain quality is first introduced, consumers may choose to strategically delay their purchasing decisions in anticipation of the product reviews of their peers. This paper investigates how the presence of social learning affects the strategic interaction between a dynamic-pricing monopolist and a forward-looking consumer population, within a simple two-period model. Our analysis yields three main insights. First, we find that the presence of social learning has significant structural implications for optimal pricing policies: In the absence of social learning, decreasing price plans are always preferred by the firm; by contrast, in the presence of social learning we find that (i) if the firm commits to a price path ex ante (preannounced pricing), an increasing price plan is typically announced, whereas (ii) if the firm adjusts price dynamically (responsive pricing), prices are initially low and may either rise or decline over time. Second, we establish that under both preannounced and responsive pricing, even though the social learning process exacerbates strategic consumer behavior (i.e., increases strategic purchasing delays), its presence results in an increase in expected firm profit. Third, we illustrate that, contrary to results reported in existing literature on strategic consumer behavior, in settings where social learning is significantly influential, preannounced pricing policies are generally not beneficial for the firm

판매촉진을 도입한 수요 불확실성 재고관리 모형

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2020. 8. 문일경.As the globalization of markets accelerates competition among companies, sales promotion, which refers to short-term incentives promoting sales of products or services, plays a prominent role. Although there are various types of sales promotions, such as price reduction, buy-x-get-y-free, and trade-in program, the common purpose is to induce the purchase of customers by offering benefits. This successful strategy has caught the attention of researchers, including operations management and supply chain management. Thus, various studies have been conducted to examine strategies for ongoing operations and to demonstrate the effects of the sales promotion, which are based on the strategic level. However, research at the tactical or operational level has been conducted insufficiently. This dissertation examines the inventory models considering (i) markdown sale, (ii) buy one get one free (BOGO), and (iii) trade-in program. First, the newsvendor model is considered. By introducing the decision variable, which represents the start time of markdown sale, the retailer can obtain the optimal combination of the start time of a markdown sale and an order quantity. Under certain conditions in a decentralized system, however, the start time of a markdown sale where the retailer obtains the highest profit is the least profitable for the manufacturer. To avoid irrational ordering behavior by a retailer against a manufacturer, a revenue-sharing contract is proposed. Second, the mobile application, ``My Own Refrigerator'', is considered in the inventory model. It enables customers to store BOGO products in their virtual storage for later use. That is, customers can drop by the store to pick up the extra freebies in the future. The promotion involves a high degree of uncertainty regarding the revisiting date because customers who buy the product do not need to take both products on the day of purchase. To deal with this uncertainty, we propose a robust multiperiod inventory model by addressing the approximation of a multistage stochastic optimization model. Third, the trade-in program is considered. It is one of the sales promotions that companies collect used old-generation products from customers and provide them with new-generation products at a discount price. It also helps to acquire the additional products which are required for the refurbishment service. A multiperiod stochastic inventory model based on the closed-loop supply chain system is proposed by incorporating the trade-in program and refurbishment service simultaneously. The stochastic optimization model is approximated to the robust counterpart, which features a deterministic second-order cone program.시장의 세계화에 따른 기업 간의 경쟁이 가속화됨에 따라, 단기 인센티브를 통해 고객의 제품 또는 서비스 구매를 유도하는 판매촉진의 역할이 중요해졌다. 가격 인하, 행사상품 증정, 트레이드인프로그램과 같은 다양한 유형의 판매촉진 전략이 존재하지만, 공통된 주요 목적은 기업이 고객에게 혜택을 제공하여 고객의 수요를 증대시키는 것이다. 판매촉진의 성공적인 전략은 경영과학 또는 공급망관리 분야를 포함한 관련 학계의 관심을 이끌었다. 지속적인 운영을 위한 전략을 검토하고 전략적 수준 계획을 기반으로 하는 판매 촉진의 효과를 입증하기 위한 다양한 연구가 수행되었습니다. 하지만 운영 수준의 소매업체 입장에서의 연구는 미흡한 실정이다. 본 논문에서는 (i) 마크 다운 (ii) buy one get one free (BOGO), 및 (iii) 트레이드인프로그램을 고려한 재고관리모형을 다룬다. 먼저, 신문가판원 모형에 마크 다운 시작 시점을 나타내는 결정 변수를 도입하여 최적의 마크 다운 시작 시점과 주문량의 조합을 제공하는 모형을 제안한다. 분산 시스템의 특정 조건에서는 소매업자가 가장 높은 이익을 얻는 시점이 제조업자에게 낮은 수익성을 야기할 수 있다. 따라서 본 연구는 제조업자에 대한 소매업자의 비합리적 주문을 막기 위한 이익분배계약을 제안한다. 이익분배계약을 통한 중앙집권화 시스템은 분산 시스템에서 얻은 이익에 비해 소매업자와 제조업자의 이익을 향상시킴을 수치실험을 통해 확인하였다. 둘째, 모바일 어플리케이션 ``나만의 냉장고''를 고려한 재고모형을 고려한다. 이 앱을 통해 BOGO 행사제품을 구매한 고객은 증정품을 구매 당일 날 가져가지 않고 미래에 재방문하여 수령할 수 있는 혜택을 받는다. 하지만 소매업자 입장에서는 고객이 증정품을 언제 수령해 갈 지에 대한 불확실성이 존재하며 이는 기존의 재고관리 운영방식에는 한계점이 있음을 시사한다. 본 연구에서는 고객의 재방문에 대한 불확실성을 고려한 복수기간 추계계획 재고모형을 수립하며 이를 효율적으로 계산하기 위한 강건최적화 모형으로 근사화하였다. 셋째, 리퍼서비스와 트레이드인프로그램을 고려한 폐회로 공급망 시스템 기반의 복수기간 재고관리모형을 제안한다. 신세대 제품, 리퍼서비스 및 트레이드인프로그램에 대한 세 가지 유형의 불확실한 수요에 대한 상관관계를 반영함에 따라 복수기간 추계계획 재고모형이 수립된다. 복수기간 추계계획 재고모형의 계산이 어렵다는 한계를 극복하고자 강건최적화 모형으로 근사화하였다.Chapter 1 Introduction 1 1.1 Sales promotion 1 1.2 Inventory management 3 1.3 Research motivations 6 1.4 Research contents and contributions 8 1.5 Outline of the dissertation 10 Chapter 2 Optimal Start Time of a Markdown Sale Under a Two-Echelon Inventory System 11 2.1 Introduction and literature review 11 2.2 Problem description 17 2.3 Analysis of the decentralized system 21 2.3.1 Newsvendor model for a retailer 21 2.3.2 Solution procedure for an optimal combination of the start time of the markdown sale and the order quantity 25 2.3.3 Profi t function of a manufacturer 25 2.3.4 Numerical experiments of the decentralized system 27 2.4 Analysis of a centralized system 35 2.4.1 Revenue-sharing contract 35 2.4.2 Numerical experiments of the centralized system 38 2.5 Summary 40 2.5.1 Managerial insights 41 Chapter 3 Robust Multiperiod Inventory Model with a New Type of Buy One Get One Promotion: "My Own Refrigerator" 43 3.1 Introduction and literature review 43 3.2 Problem description 51 3.2.1 Demand modeling 52 3.2.2 Sequences of the ordering decision 54 3.3 Mathematical formulation of the IMMOR 56 3.3.1 Mathematical formulation of the IMMOR under the deterministic demand 58 3.3.2 Mathematical formulation of the IMMOR under the stochastic demand 58 3.3.3 Distributionally robust optimization approach for the IMMOR 60 3.4 Computational experiments 76 3.4.1 Experiment 1: tractability of the RIMMOR 77 3.4.2 Experiment 2: robustness of the RIMMOR 78 3.4.3 Experiment 3: e ect of duration of the expiry date under the different customers' revisiting propensities 78 3.5 Summary 83 3.5.1 Managerial insights 83 Chapter 4 Robust Multiperiod Inventory Model Considering Refurbishment Service and Trade-in Program 85 4.1 Introduction 85 4.2 Literature review 91 4.2.1 Effects of the trade-in program and strategic-level decisions for the trade-in program 91 4.2.2 Inventory or lot-sizing model in a closed-loop supply chain system 94 4.2.3 Distinctive features of this research 97 4.3 Problem description 100 4.3.1 Demand modeling 103 4.3.2 Decision of the inventory manager 105 4.4 Mathematical formulation 108 4.4.1 Mathematical formulation of the IMRSTIP under the deterministic demand model 108 4.4.2 Mathematical formulation of the IMRSTIP under the stochastic demand model 110 4.4.3 Distributionally robust optimization approach for the IMRSTIP 111 4.5 Computational experiments 125 4.5.1 Demand process 125 4.5.2 Experiment 1: tractability of the RIMRSTIP 128 4.5.3 Experiment 2: approximation error from the expected value given perfect information 129 4.5.4 Experiment 3: protection against realized uncertain factors 130 4.5.5 Experiment 4: di erences between modeling demands from VARMA and ARMA 131 4.5.6 Experiments 5 and 6: comparisons of backlogged refurbishment service with or without trade-in program 133 4.6 Summary 136 Chapter 5 Conclusions 138 5.1 Summary 138 5.2 Future research 140 Bibliography 142 Chapter A 160 A.1 160 A.2 163 A.3 163 A.4 164 A.5 165 A.6 166 Chapter B 168 B.1 168 B.2 171 B.3 172 Chapter C 174 C.1 174 C.2 174 국문초록 179Docto

Dynamic pricing with the counter-conformity, conformity and non-conformity of consumer behavior

Confronted with well-informed consumers, the firms have to take everything into consideration. Through the classic game theory, pricing mechanism is discussed with different characteristics of consumer behavior. The consumer population is heterogeneous along two dimensions: they may have an inclination towards the obedience of the public and different degrees of patience. After introducing the price deviation variables, we demonstrate that heterogeneity in both inclination and patience is important because they jointly determine the structure of optimal pricing policies. The numerical example shows that the markdown degree, the expected purchasing amount of consumers and the expected profits of the firm are increasing with the increase of the proportion of counter-conformity consumers. And we also examine whether the discount rate of capital, counter-conformity consumers and myopic consumers will have an impact on the sales. In particular, when the discount rate and the proportion of the conformity customers are too high, the expected profits of the firm are increasing mildly with the increase of the proportion of myopic customers. Therefore, the discount rate and characteristics of consumer behavior should be considered together to maximize the revenue of firms

Consumer Returns Policies and Supply Chain Performance

This paper develops a model of consumer returns policies. In our model, consumers face valuation uncertainty and realize their valuations only after purchase. There is also aggregate demand uncertainty, captured using the conventional newsvendor model. In this environment, consumers decide whether to purchase and then whether to return the product, whereas the seller sets the price, quantity, and refund amount. Using our model, we study the impact of full returns policies (e.g., using 100% money-back guarantees) and partial returns policies (e.g., when restocking fees are charged) on supply chain performance. Next, we demonstrate that consumer returns policies may distort incentives under common supply contracts (such as manufacturer buy-backs), and we propose strategies to coordinate the supply chain in the presence of consumer returns. Finally, we explore several extensions and demonstrate the robustness of our findings

Online and Offline Information for Omnichannel Retailing

This paper studies how retailers can effectively deliver online and offline information to omnichannel consumers who strategically choose whether to gather information online or offline and whether to buy products online or offline. Information resolves two types of uncertainty: product value uncertainty (i.e., consumers realize valuations when they inspect the product in store, but may end up returning the product when they purchase online) and availability uncertainty (i.e., store visits are futile when consumers encounter stockouts). We consider three information mechanisms: physical showrooms allow consumers to learn valuations anytime they visit the store, even during stockouts; virtual showrooms give consumers online access to an imperfect signal of their valuations; availability information provides real-time information about whether the store has a product in stock. Our main results follow. First, physical showrooms may prompt retailers to reduce store inventory, which increases availability risk and discourages store patronage. Second, virtual showrooms may increase online returns and hurt profits, if they induce excessive customer migration from store to online channels. Third, availability information may be redundant when availability risk is low and may render physical showrooms ineffective when implemented jointly. Finally, when customers are homogeneous, these mechanisms may not exhibit significant complementarities and the optimal information structure may involve choosing only one of the three

Optimal Pricing and Promotion Strategies in IT-Enabled Retail Environment

Ph.DDOCTOR OF PHILOSOPH